Ben is 3 times as old as Gabriela. Twelve years ago, Ben was 5 times as old as Gabriela. How old is Ben now?
Explanation: We can use the given information to write down two equations that describe the ages of Ben and Gabriela. Let Ben's current age be $b$ and Gabriela's current age be $g$ The information in the first sentence can be expressed in the following equation: $b = 3g$ Twelve years ago, Ben was $b - 12$ years old, and Gabriela was $g - 12$ years old. The information in the second sentence can be expressed in the following equation: $b - 12 = 5(g - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $g$ and substitute it into our second equation. Solving our first equation for $g$ , we get: $g = b / 3$ . Substituting this into our second equation, we get: $b - 12 = 5($ $(b / 3)$ $- 12)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 12 = \dfrac{5}{3} b - 60$ Solving for $b$ , we get: $\dfrac{2}{3} b = 48$ $b = \dfrac{3}{2} \cdot 48 = 72$.